Algorithm portfolio selection as a bandit problem with unbounded losses

We propose a method that learns to allocate computation time to a given set of algorithms, of unknown performance, with the aim of solving a given sequence of problem instances in a minimum time. Analogous meta-learning techniques are typically based on models of algorithm performance, learned during a separate offline training sequence, which can be prohibitively expensive. We adopt instead an online approach, named GAMBLETA, in which algorithm performance models are iteratively updated, and used to guide allocation on a sequence of problem instances. GAMBLETA is a general method for selecting among two or more alternative algorithm portfolios. Each portfolio has its own way of allocating computation time to the available algorithms, possibly based on performance models, in which case its performance is expected to improve over time, as more runtime data becomes available. The resulting exploration-exploitation trade-off is represented as a bandit problem. In our previous work, the algorithms corresponded to the arms of the bandit, and allocations evaluated by the different portfolios were mixed, using a solver for the bandit problem with expert advice, but this required the setting of an arbitrary bound on algorithm runtimes, invalidating the optimal regret of the solver. In this paper, we propose a simpler version of GAMBLETA, in which the allocators correspond to the arms, such that a single portfolio is selected for each instance. The selection is represented as a bandit problem with partial information, and an unknown bound on losses. We devise a solver for this game, proving a bound on its expected regret. We present experiments based on results from several solver competitions, in various domains, comparing GAMBLETA with another online method.